Finite Group Databasebeta

← #15758988

Subgroups — #15758988

Order 3328.

622 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117454C211yesmaximal, characteristic, complemented
2#13113404C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic, complemented
4#13112703C212yesmaximal, complemented
5C13×#2618C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C2211yescharacteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C2×#88180—21no—
10C13×#398C412yescomplemented
11C13×#396—22no—
12C13×#394C412yescomplemented
13C13×#386—21no—
14C13×#380C2211yescharacteristic
15#11718873—21no—
16#11718873C2212yes—
17C2×C22⋊#1055C2212yes—
18#11718646—24no—
19#11718129—24no—
20#11718120—22no—
21C22×D4×C13—21no—
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C13×#123—42no—
27C13×#123—42no—
28C13×#121—22no—
29C13×#121—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C412yes—
36C2×C13×C4⋊C4D412yes—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C22⋊Dic13—22no—
42#88180—42no—
43#88180—42no—
44C2×C4⋊Dic13—22no—
45C2×C4⋊Dic13—22no—
46C2×C4⋊Dic13—22no—
47C2×C4×Dic13—22no—
48C22×#1055—22no—
49C13×#95—22no—
50C13×#95C2×C412yes—
51#88071—22no—
52#88071D414yes—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#9204—131nomaximal, Sylow
56C24×C13—21no—
57C24×C13C2×D411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—81no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—22no—
74C22×C4×C13—81no—
75C22×C4×C13—81no—
76C22×C4×C13C22⋊C412yes—
77C22×C4×C13C22⋊C412yes—
78C22×C4×C13D812yes—
79C22×C4×C13SD1612yes—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4112yes—
84C22×Dic13—24no—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—44no—
89C13×C4⋊C4—81no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—82no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C4⋊Dic13—44no—
98C4⋊Dic13—82no—
99C4⋊Dic13—82no—
100C4×Dic13—44no—
101C2×#1055—42no—
102C2×#1055—82no—
103#2618D1311yescharacteristic
104#2316—131no—
105#1519—132no—
106C2×#324—131no—
107#1289—132no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—42no—
111C23×C13—42no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13#12011yescharacteristic
117C23×C13#12311yescharacteristic
118C23×C13C2×D811yescharacteristic
119C23×C13C2×SD1611yescharacteristic
120C23×C13AGL(1,ℤ/8)11yescharacteristic
121C23×C13#13711yescharacteristic
122D4×C13—82no—
123D4×C13—81no—
124D4×C13—81no—
125D4×C13—81no—
126D4×C13—81no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—81no—
147C2×C4×C13#10214yes—
148C2×C4×C13C4×D412yes—
149C2×C4×C13#12112yes—
150C2×Dic13—44no—
151C2×Dic13—44no—
152C2×Dic13—44no—
153#1055—82no—
154C2×#123—21no—
155C2×#121C2×D1311yescharacteristic
156C2×#117—261no—
157C22×C4⋊C4C2×D1311yescharacteristic
158C2×C22⋊C8—132no—
159#398Dic1312yescomplemented
160#396—22no—
161#394Dic1312yescomplemented
162#389—264no—
163#386—21no—
164#380—132no—
165#380—261no—
166#380C2×D1311yescharacteristic
167#327—264no—
168#324—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—82no—
180C22×C13—82no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13#38611yescharacteristic
185C22×C13C2×#10211yescharacteristic
186C22×C13#41711yescharacteristic
187C22×C13#44711yescharacteristic
188C22×C13#44811yescharacteristic
189C22×C13#48011yescharacteristic
190C22×C13#48111yescharacteristic
191C4×C13—24no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—42no—
195C4×C13—82no—
196C4×C13—81no—
197Dic13—84no—
198C22×D4—21no—
199C22×D4C2×Dic1311yescharacteristic
200C23×C4C22⋊D1311yescharacteristic
201C23×C4C22⋊D1311yescharacteristic
202C23×C4C22×D1311yescharacteristic
203C22×C8—262no—
204#123—42no—
205#123—42no—
206#121—22no—
207#121—22no—
208#117—522no—
209#117—522no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—262no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4—262no—
217C2×C4⋊C4C2×Dic1311yescharacteristic
218C2×C4⋊C4C2×Dic1312yes—
219C2×C4⋊C4C22⋊D1312yes—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—262no—
225C2×C42—262no—
226C22⋊C8—262no—
227C22⋊C8—262no—
228#95—22no—
229#95—134no—
230#95—262no—
231#95C2×Dic1312yes—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—161no—
239C2×C13#187411yescharacteristic
240C2×C13#191211yescharacteristic
241C2×C13#191311yescharacteristic
242C24—21no—
243C24C2×C22⋊D1311yescharacteristic
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—81no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—264no—
263C22×C4#610412yes—
264C22×C4#610512yes—
265C22×C4C22⋊Dic1312yes—
266C22×C4C22⋊Dic1312yes—
267C22×C4D4×D1312yes—
268C22×C4#612912yes—
269C22×C4C22×Dic1311yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271C2×C8—522no—
272C2×C8—1042no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—22no—
276C4⋊C4—44no—
277C4⋊C4—81no—
278C4⋊C4—524no—
279C4⋊C4—1042no—
280C4⋊C4—1042no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C22⋊C4—82no—
286C22⋊C4—522no—
287C22⋊C4—522no—
288C42—524no—
289C13#920411yescharacteristic, complemented, Sylow
290C23—41no—
291C23—41no—
292C23—42no—
293C23—42no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×#610411yescharacteristic
298C23C2×#610511yescharacteristic
299C23#8818911yescharacteristic
300C23#8819111yescharacteristic
301C23#8820311yescharacteristic
302C23#8820511yescharacteristic
303C23C2×C22⋊Dic1311yescharacteristic
304D4—82no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—81no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—524no—
330C2×C4—524no—
331C2×C4—524no—
332C2×C4#8807214yes—
333C2×C4D4×Dic1312yes—
334C2×C4#8819312yes—
335C8—1042no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—82no—
347C22—82no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22#1171869411yescharacteristic
352C22#1171869511yescharacteristic
353C22#1171869711yescharacteristic
354C22#1171870111yescharacteristic
355C22C2×#8807211yescharacteristic
356C22#1171888111yescharacteristic
357C22#1171889311yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—82no—
363C4—81no—
364C4—1044no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—161no—
372C2#1311515411yescharacteristic
373C2#1311537411yescharacteristic
374C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2618C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2618D13
hypocenterC13#9204
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2618

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13117454C2semidirect
3. C2×#11718120C2semidirect
4. #13112703C2semidirect
10. C13×#398C4semidirect
12. C13×#394C4semidirect
159. #398Dic13semidirect
161. #394Dic13semidirect
289. C13#9204semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131174542
#131134042
C2×#117181202
#131127032
C13×#26182
#920413